Exercise 10 Page 459

We want to find the value of x. Notice that the triangles have two pairs of congruent angles. Therefore, by the Angle-Angle Similarity Theorem, the triangles are similar.

Since the figures are similar, their corresponding sides are also similar. Let's identify them.

• There is only one side in each triangle which is opposite to the right angle. These are corresponding sides.
• In each triangle, there are two sides included between the right angle and an acute angle. From these, the shorter sides in each triangle are corresponding, and the longer sides in each triangle are corresponding as well.

The ratio between corresponding sides is always the same. With this information we can write an equation in terms of x. 8/24=x/10 Let's solve the above equation!

8/24=x/10

CrossMult

Cross multiply

8 * 10 = 24 * x

▼

Solve for x

Multiply

Multiply

80 = 24x

RearrangeEqn

Rearrange equation

24x=80

DivEqn

.LHS /24.=.RHS /24.

x=80/24

ReduceFrac

a/b=.a /8./.b /8.

x=10/3