Two triangles are similar. The perimeter of the larger triangle is 94.5 inches
SOLUTION:
Given, Two triangles are similar. Â
The height of the smaller triangle is 6 inches and the corresponding height of the larger triangle is 15 inches. Â
The perimeter of the smaller triangle is 37.8 inches, Â
We have to find what is the perimeter of the larger triangle?
We know that, for similar triangles, ratio of heights = ratio of perimeters
[tex]\begin{array}{l}{\text { Then, } \frac{\text {height of } 1 \text {st triangle}}{\text {height of } 2 \text {nd} \text { triangle}}=\frac{\text {perimeter of } 1 \text {st triangle}}{\text {perimeter of } 2 n d \text { triangle}}} \\\\ {\frac{6}{15}=\frac{37.8}{\text { perimeter of } 2 \text {nd triangle}}}\end{array}[/tex]
[tex]\begin{array}{l}{\text { Perimeter of } 2^{\text {nd triangle }} \times 6=37.8 \times 15} \\\\ {\text { Perimeter of } 2^{\text {nd triangle }}=37.8 \times \frac{15}{6}=37.8 \times \frac{5}{2}=\frac{189}{2}=94.5}\end{array}[/tex]
Hence, the perimeter of the larger triangle is 94.5 inches
