Question

The perimeter of an isosceles triangle is 32 cm. If each equal side is $\frac{5}{6}$ th of the base, find the area of the triangle.

Approach

Isosceles triangle with perimeter $32$ cm and each equal side $\frac{5}{6}$ of the base. Let base $= y$ , equal sides $= x = \frac{5}{6} y$ . From $2 x + y = 32$ : $2 \cdot \frac{5}{6} y + y = 32$ , giving $y = 12$ cm, $x = 10$ cm. Semi-perimeter $s = 16$ cm. Area $= 16 \cdot 6 \cdot 6 \cdot 4 = 48$ cm $^{2}$ .

Step-by-step working

1
Let base $= y$ and equal sides $= x = \frac{5}{6} y$ . Perimeter: $2 x + y = 32$
1 mark
2
Substitute: $\frac{5}{3} y + y = 32 \Rightarrow \frac{8 y}{3} = 32 \Rightarrow y = 12$ cm
1 mark
3
$x = 10$ cm. Sides are $10, 10, 12$ cm
1 mark
4
Semi-perimeter $s = 16$ cm
0.5 marks
5
Area $= 16 \times 6 \times 6 \times 4 = 48$ cm $^{2}$
1.5 marks

Concepts used

isosceles triangleperimeterareafind areaheron's formula

Approach

Step-by-step working

Concepts used

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