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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q30. (page 432)

An isosceles triangle has sides that are $5 c m, 5 c m$ and8cmlong. Find its area and the lengths of the three altitudes.

Short Answer

Expert verified

The area of triangle is $12 s q . u n i t$ and the length of altitudes are $3, 4.8, 4.8$

Step by step solution

01

Step 1. Draw the diagram.

02

Step 2. Concept used.

We can use Pythagorean Theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

$\begin{array}{l} 5^{2} = 4^{2} + h^{2} \\ h^{2} = 25 - 16 \\ h^{2} = 9 \\ h = 3 \end{array}$

03

Step 3. Use the concept of area of triangle.

Area of $△ A B C$ can be found using the formula

$\begin{array}{l} b = B C = 8 \\ h = 3 \\ A = \frac{1}{2} b h \\ A = \frac{1}{2} (8) (3) \\ A = 12 s q . u n i t \end{array}$

04

Step 4. Find the altitudes.

The length of altitude $B E$

$\begin{array}{l} b = 5 \\ h = ? \\ A = 12 \\ A = \frac{1}{2} b h \\ 12 = \frac{1}{2} (5) (h) \\ 24 = 5 h \\ h = \frac{24}{5} \\ h = 4.8 \end{array}$

Similarly, The length of altitude $C F$ is $4.8$

Therefore, the Area is $12 s q . u n i t$

The length of altitudes are $3, 4.8, 4.8.$

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Most popular questions from this chapter

a. Find the ratio of the areas of $△ Q R T$ and $△ Q T S$ .

b. If the area of $△ Q R S$ is240. Find the length of the altitude from sto. $\overset{\leftrightarrow}{Q R}$

The base of a triangle is 1cm longer than its altitude. If the area of the triangle is $210 c m^{2}$ , how long is the altitude ?

The base of a rectangle is $4 k - 1$ and height $k + 2$ . What is the area?

a. Find the area of the right triangle in terms of a and b.

b. Find the area of the right triangle in terms of c and h.

c. Solve for hin terms of the other variables.

d. A right triangle has legs 6 and 8. Find the lengths of the altitude and the median to the hypotenuse.

Find the area of each figure:

An equilateral triangle with sides $8 f t$

See all solutions

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