Question

HOTS
1. Find the area of a triangle whose sides are in
mangle whose sides are in the ratio 5 : 12:13 and its perimeter is 60
cm.​

Answer 1

Given,

ratio = 5:12:13

let the common multiple = x

thus sides= 5x,12x,13x

perimeter = sum of all sides.

60= 5x+12x+13x

60= 30x

x= 2

thus,

sides = 5x= 10cm

12x= 24cm

13x= 26cm

S= 24+26+10/2 = 30 cm

thus by herons formula,

√s(s-a)(s-b)(s-c) = √30(20)(6)(4)= √14400= 120cm²

Answer 2

$let \: the \: sides \: be \: 5x \: 12x \: 13x \\ \\ according \: to \: question \\ 60 = 5x + 12x + 13x \\ 60 = 30x \\ 60 \div 30 = x \\ x = 2 \\ sides \: are \\ 5 \times 2 = 10cm \\ 12 \times 2 = 24cm \\ 13 \times 2 = 26cm$

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