Question

The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is:
(a) 10root3 cm2
(b) 100root3 cm2
(c) 300 cm2
(d) 50root3 cm2​

Answer 1

Question :-

The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is:

(a) 10root3 cm²

(b) 100root3 cm²

(c) 300 cm²

(d) 50root3 cm²

Solution :-

Given :-

• Sides of triangle : 5cm, 7cm and 8cm.

Need to find :-

• Area of triangle

Here, we the sides of triangle and need to find the area of triangle, then we firstly find perimeter of triangle then find semi - perimeter ($\because$ In the area of triangle formula we need semi - perimeter.)

Perimeter of triangle :-

$\sf:\longmapsto{Perimeter_{(\triangle) }= a + b + c}$

Here, a, b, and c are the sides of triangle.

$\sf:\longmapsto{Perimeter_{(\triangle)} =5 + 7 + 8 } \\ \\ \bf:\longmapsto \red{Perimeter_{(\triangle)} =20cm } \:$

Semi - perimeter of triangle :-

$\sf:\longmapsto{Semi - Perimeter_{(\triangle)} =\frac{Perimeter}{2} }$

Perimeter is already founded.

$\sf:\longmapsto{Semi - Perimeter_{(\triangle)} = \frac{20}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{Semi - Perimeter_{(\triangle)} =10cm }$

Area of triangle :-

$\sf:\longmapsto{Area_{(\triangle)} = \sqrt{s(s-a)(s-b)(s-c)}}$

Here, s means semi - perimeter and a, b, and c are already given.

$\sf:\longmapsto{Area_{(\triangle)} = \sqrt{10(10 - 5)(10 - 7)(10 - 8)} } \\ \\ \sf:\longmapsto{Area_{(\triangle)} = \sqrt{10(5)(3)(2)} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{Area_{(\triangle)} = \sqrt{10(30)} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{Area_{(\triangle)} = \sqrt{300} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

We can write √300 = √100 × 3

$\sf:\longmapsto{Area_{(\triangle)} = \sqrt{100 \times 3} }$

We know that, √100 = 10

$\bf:\longmapsto \red{Area_{(\triangle)} = 10 \sqrt{3}cm {}^{2} }$

Hence, option (1) is right answer.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Learn more from brainly :

the length of the sides of a triangle area in the ratio 3 :4 : 5 and its perimeter is 144 CM the area of the triangle is a)6 8 4 cm square b)6 64 CM square c)7 64 CM square d)864 CM square.

https://brainly.in/question/4141735