Question

In an isosceles triangle ABC. The measure of side AB and base BC are in the ratio 13: 11: . If perimeter of triangle ABC is 259 cm. Find the measure of all sides​

Answer 1

Given AB : BC = 13 : 11 ( Given )

Since AB = AC, then

=> AB : AC : BC = 13 : 13 : 11

Let X be the constant ratio

AB : AC : BC = 13x : 13x : 11x

The perimeter is 259 cm

13x + 13x + 11 = 259 cm

37x = 259

X = 259 ÷ 37

X = 7

13x = ( 13)7 = 91 cm

11x = 11(7) = 77 cm

Answer = The sides are 91 cm, 91 cm and 77 cm.

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Answer 2

In triangle ABC
AB = AC (sides of isosceles traiangle)

AB:BC:: 13:11 .... given
AB / BC = 13/11
11AB = 13BC
11AB - 13 BC = 0 ...... equation 1

Perimeter =259
AB + BC + AC = 259
AB + AB + BC = 259 ( since AB= AC)
2AB + BC = 259 .... equation 2

Multiplying equation 2 by 13 we get
26AB + 13AC = 3,367.... equation 3

Adding equation 1 and 3 we get
11AB - 13BC = 0
+ 26AB + 13BC = 3367
=. 37AB. = 3367
( + 13BC and -13BC will cancel each other )

37AB = 3367
AB = 3367/37
AB= 91 units

AC = AB = 91 units

Substituting value Of AB in equation 2
2AB + BC = 259
2(91) + BC = 259
182 + BC = 259
BC = 259 -182
BC = 77

Thereby the measures are
AB= 91 units
AC = 91 units
BC = 77 units