Math / Geometry

QuestionIf these two shapes are similar, what is the measure of the missing length $w$ ? $w=$ $\square$ yards Submit

Studdy Solution

STEP 1

1. The two triangles are similar, which means their corresponding sides are proportional.
2. The sides of the triangles are labeled with given lengths, and we need to find the missing length $w$ of the smaller triangle.
3. The proportionality ratio between the corresponding sides of similar triangles is consistent.

STEP 2

1. Determine the ratio of the corresponding sides of the two triangles.
2. Set up a proportion using the ratio of the corresponding sides.
3. Solve the proportion to find the missing length $w$ .

STEP 3

Determine the ratio of the base of the smaller triangle to the base of the larger triangle.
$\text{Ratio} = \frac{\text{base of smaller triangle}}{\text{base of larger triangle}} = \frac{3 \text{ yards}}{9 \text{ yards}}$

STEP 4

Simplify the ratio obtained in STEP_1.
$\text{Ratio} = \frac{3}{9} = \frac{1}{3}$

STEP 5

Set up a proportion using the ratio of the corresponding sides of the two triangles. The corresponding height of the larger triangle is given as 3 yards. The height of the smaller triangle is $w$ .
$\frac{\text{height of smaller triangle}}{\text{height of larger triangle}} = \frac{w}{3 \text{ yards}}$

STEP 6

Since the triangles are similar, the ratio of the heights must be the same as the ratio of the bases.
$\frac{w}{3 \text{ yards}} = \frac{1}{3}$

STEP 7

Solve the proportion to find $w$ .
$w = 3 \text{ yards} \times \frac{1}{3}$

STEP 8

Simplify to determine the value of $w$ .
$w = 1 \text{ yard}$
The measure of the missing length $w$ is 1 yard.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms