Question

The area of the triangle with sides 60 cm, 100 cm and 140 cm is of the form 1500 √x cm
Find the value of x.​

Answer 1

Answer:

9405 - maybe

Step-by-step explanation:

Use heron's formula & you will get the answer.

Hope it helps.

Thank you.

Answer 2

Given :-

♦ Sides of a triangle = 60 cm, 100cm, 140cm

♦ Area = 1500 √x cm²

To find :-

x = ?

Method :-

$\bf{ apply \: Heron's \: formula} \\ \\ \sf \: {here} \\ \tt{s = semi \: perimeter = \frac{60 + 100 + 140}{2} } \\ \sf{s = 150 \: cm } \\ \\ \sf{a = first \: side = 60 \: cm} \\ \sf{b = second \: side =100 \: cm } \\ \sf{c = third \: side = 140 \: cm} \\ \\ \sf{Area = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ \implies \sf Area = \sqrt{150(150 - 60)(150 - 100)(150 - 140)} \\ \\ \implies \sf{Area = \sqrt{150 \times 90 \times 50 \times 10} } \\ \\ \implies \sf{Area = \sqrt{15 \times 9 \times 5 \times 100 \times 100} } \\ \\ since \: 9 \: and \:100 \: are \: perfect \: squares \\ \\ \sf{area = 3 \times 10 \times 10 \sqrt{15 \times 5} } \\ \\ \implies \sf{Area = 300 \sqrt{75} } \\ \\ \implies \sf{Area = 300 \sqrt{25 \times 3} } \\ \\ \implies \sf{Area = 300 \times 5 \sqrt{3} } \\ \\ \therefore \boxed{ \boxed{ \bf{Area = 1500 \sqrt{3} \: cm {}^{2} }}}$

x = 3