Question

A triangular garden has two equal sides
and the length of one of its side is 50
metres. Find the length of the two
equal sides, if the cost of paving the
garden is Rs 3500 at Rs 2.50 per
square metre.
(a) 63.11 m
(b) 61.33 m
(C) 64.39 m
(d) 65.33 m​

Answer 1

sum of triangle= 180

length of one side =50

length of other two equal parts =180-50= 130

length one side =130÷2= 65

Answer 2

The length of two equal sides is 61.33 metres. Option B is correct

Solution:

Given that the triangle has two equal sides. Thus it is a isosceles triangle

$\text { Area of the triangular garden }=\frac{\text {total cost of pavement}}{\text {cost per square meter}}$

Given that total cost = Rs 3500

cost per square meter = 2.50

$\text { Area of the triangular garden }=\frac{3500}{2.50}=1400$

Given that one side of triangle = 50 metres

Length of other two sides = ?

The area of isosceles triangle is given as:

$\text { area }=\frac{1}{2} \mathrm{b} \sqrt{\mathrm{a}^{2}-\frac{\mathrm{b}^{2}}{4}}$

Where "a" indicates length of equal sides

Substituting the values, we get,

Here area = 1400 ; a = ? ; b = 50

$\begin{array}{l}{112=\sqrt{4 a^{2}-50^{2}}} \\\\ {112^{2}=4 a^{2}-2500} \\\\ {a^{2}=3761} \\\\ {\mathrm{a}=61.33}\end{array}$

Hence the length of two equal sides is 61.33 metres. Thus option B is correct

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