Area and Perimeter Practice Test 1

Let base of the right angled triangle = x cm; then
height = 60 – 26 – x = 34 – x
Since, ${\mathit{x}}^2$ + (34 – x)2 = (26)2
⇒ ${\mathit{x}}^2$ + 1156 – 68x + x2 = 676
⇒ $2{\mathit{x}}^2$ – 68x + 480 = 0
⇒ ${\mathit{x}}^2$ –34x + 240 = 0
⇒ (x –24) (x – 10) = 0
Either, x = 24 or 10 then height = 34 – x = 10 or , 24
Since, area of right angled triangle = $\frac{1}{2}$ × 24 × 10 = $120\mathit{c}{\mathit{m}}^2$