Chapter 10: Q 289. (page 1237)

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.
A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and
length of the base.

Short Answer

Expert verified

The base of the triangle is $54 c m$ and the height of the triangle is $13 c m .$

Step by step solution

Given information.

The given statement is:

A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Set up an equation such that the length of the base is two centimeters longer than four times the height.

Let the height of the triangle be $x .$

$B a s e = 4 \times h e i g h t + 2 B a s e = 4 x + 2$

Use the formula of the area of the triangle.

$A r e a = \frac{1}{2} \times b a s e \times h e i g h t 351 = \frac{1}{2} \times (4 x + 2) x 351 = \frac{1}{2} \times 4 x^{2} + 2 x 351 = \frac{x}{2} (4 x + 2)$

Multiply both sides of the equation by 2.

$2 \times 351 = 2 \times \frac{x}{2} (4 x + 2) 702 = 4 x^{2} + 2 x 4 x^{2} + 2 x - 702 = 0$

Use the quadratic formula.

The quadratic formula for the equation $a x^{2} + b x + c = 0 i s x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} .$

Now we compare the given equation with the standard form we get $a = 4, b = 2 a n d c = - 702 .$

$x = \frac{- 2 \pm \sqrt{{(2)}^{2} - 4 (4) (- 702)}}{2 (4)} x = \frac{- 2 \pm \sqrt{11, 236}}{8} x = \frac{- 2 \pm \sqrt{106}}{8} x = 13, - 13.5$

Because the base cannot be negative. So, the base isrole="math" localid="1653654547253" $13 (4) + 2 = 54 c m a n d t h e h e i g h t i s 13 c m .$

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In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.
A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and
length of the base.

Short Answer

Step by step solution

Given information.

Set up an equation such that the length of the base is two centimeters longer than four times the height.

Use the formula of the area of the triangle.

Use the quadratic formula.

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height andlength of the base.

Short Answer

Step by step solution

Given information.

Set up an equation such that the length of the base is two centimeters longer than four times the height.

Use the formula of the area of the triangle.

Use the quadratic formula.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.
A triangular banner has an area of 351 square centimeters. The length of the base is two centimeters longer than four times the height. Find the height and
length of the base.