What is the area of a right-angled triangle? i. the perimeter of the triangle is 30 cm. ii. the ratio between the base and the height of the triangle is 5 : 12. iii. the area of the triangle is equal to the area of a rectangle of length 10 cm?
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the area of a right angled triangle is (1/2)*base*height
here base = 5m cm,height=12m cm
1) when the perimeter of the triangle is 30 cm
so in a right angled triangle
perimeter = a+b+root (a^2+b^2) where a=height b= base
ie 30=12m+5m+root [(12m)^2+(5m)^2]
=17m+13m=30m
or 30=30m
or m=1
so base = 5*1=5cm
height =12*1=12 cm
so the area is (1/2)*5*12=30 cm sq
again given length of the rectangle is 10 cm
let breadth of the rectangle is y cm
it is equal to the area of that triangle given
so 30=10y or y = 3
so breadth of the rectangle is 3 cm
here base = 5m cm,height=12m cm
1) when the perimeter of the triangle is 30 cm
so in a right angled triangle
perimeter = a+b+root (a^2+b^2) where a=height b= base
ie 30=12m+5m+root [(12m)^2+(5m)^2]
=17m+13m=30m
or 30=30m
or m=1
so base = 5*1=5cm
height =12*1=12 cm
so the area is (1/2)*5*12=30 cm sq
again given length of the rectangle is 10 cm
let breadth of the rectangle is y cm
it is equal to the area of that triangle given
so 30=10y or y = 3
so breadth of the rectangle is 3 cm
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