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2 years ago

The perimeter of a right angled triangle is 56 cm and its hypotenuse is 25 cm. Find the area of triangle.

Mathematics

1 answer:

Daniel [21]2 years ago

6 0

Perimeter = 56
Hypo = 25
So 56-25 = 31 (for two side)
for one side = 31/2 = 15.5

so area = 1/2 x base x height

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2 years ago

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disa [49]

Answer:

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Area = 30 square units

Step-by-step explanation:

Given

Vertices

A(2,8), B(16,2) and C(6,2)

WE have to determine the lengths of all sides before finding the perimeter and area.

The formula of modulus is:

$d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\$

So the perimeter is:

$Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units$

Using hero's formula,

$s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units$

Rounding off will give us 30 square units ..

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2 years ago

The perimeter of a right angled triangle is 56 cm and its hypotenuse is 25 cm. Find the area of triangle.​

The perimeter of a right angled triangle is 56 cm and its hypotenuse is 25 cm. Find the area of triangle.