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Chapter 9: Q. 201 (page 919)

A triangle with area 45 square inches has a height that is two less than four times the base Find the base and height of the triangle.

Short Answer

Expert verified

The height of the triangle is 18 inches and the base is 5 inches.

Step by step solution

01

Step 1. Given information

A triangle having height two less than four times the base. Its area is 45 square inches.

Find its the base and height.

02

Step 2. Calculation

Consider base of the triangle is b. So, height of the triangle is 4b-2.

Area of triangle is 45 square inches.

So the equation becomes,

45=124b-2b

Multiply by 2 on both sides.

90=4b2-2b

Form the quadratic equation and solve.

4b2-2b-90=022b2-b-45=0

03

Step 3. Solve the equation

Divide by 2 on both sides.

2b2-b-45=0

Solve the quadratic equation.

2b2-10b+9b-45=02b+9b-5=0

Use the Zero Product Property .

2b+9=0⇒b=-92

b-5=0⇒b=5

Distance can not be negative.

04

Step 4. Conclusion

As b=5

Base is 5 and height is4×5-2=18

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