# Isosceles triangle

The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.

Result

S =  588 cm2

#### Solution:

$o=112 \ \text{cm} \ \\ a:b=6:5 \ \\ o=a+2b \ \\ 6a/5=b \ \\ o=a + 2 \cdot \ 5a/6 \ \\ a=o / (1+2 \cdot \ 5/6)=112 / (1+2 \cdot \ 5/6)=42 \ \text{cm} \ \\ b=5 \cdot \ a/6=5 \cdot \ 42/6=35 \ \text{cm} \ \\ o_{1}=a+2 \cdot \ b=42+2 \cdot \ 35=112 \ \text{cm} \ \\ h=\sqrt{ b^2-(a/2)^2 }=\sqrt{ 35^2-(42/2)^2 }=28 \ \text{cm} \ \\ S=a \cdot \ h/2=42 \cdot \ 28/2=588 \ \text{cm}^2$

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