Math  /  Geometry

QuestionX 25 yd X = 7. १ 12 yd 15 yd

Studdy Solution

STEP 1

1. We have two triangles, one larger and one smaller.
2. The sides of the larger triangle are x x and 25 yards.
3. The sides of the smaller triangle are 12 yards and 15 yards.
4. The triangles are similar, meaning their corresponding sides are proportional.

STEP 2

1. Identify the relationship between the triangles.
2. Set up a proportion using the corresponding sides of the triangles.
3. Solve the proportion to find the value of x x .

STEP 3

Identify that the triangles are similar. Similar triangles have corresponding angles that are equal and corresponding sides that are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is the same.

STEP 4

Set up a proportion using the corresponding sides of the triangles. The sides of the larger triangle are x x and 25 yards, and the sides of the smaller triangle are 12 yards and 15 yards. The proportion is:
x12=2515 \frac{x}{12} = \frac{25}{15}

STEP 5

Solve the proportion to find the value of x x . Cross-multiply to solve for x x :
x15=1225 x \cdot 15 = 12 \cdot 25

STEP 6

Calculate the right side of the equation:
1225=300 12 \cdot 25 = 300
So the equation becomes:
15x=300 15x = 300

STEP 7

Solve for x x by dividing both sides of the equation by 15:
x=30015 x = \frac{300}{15}

STEP 8

Calculate the division:
x=20 x = 20
The value of x x is:
20 \boxed{20}

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