Advertisements
Advertisements
प्रश्न
The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.
उत्तर
Let ABC be a right-angled triangle.
Since the perimeter of the right triangle is 60 cm,
AB + BC +CA = 60 cm
⇒ AB + BC + 25 = 60
⇒ AB + BC = 35 cm .....(1)
In ∆ABC,
AB2 + BC2 = CA2
⇒ (AB + BC)2 − 2(AB)(BC) = (25)2
⇒ (35)2 − 2(AB)(BC) = (25)2 [From (1)]
⇒ (35 − 25)(35 + 25) = 2(AB)(BC)'
⇒ (AB)(BC) = 300
Now,
Area of ∆ABC= `1/2`×AB×BC=`1/2`×300=150 cm2
Hence, the area of the triangle is 150 cm2.
APPEARS IN
संबंधित प्रश्न
The vertices of ∆ABC = are A (4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively such that `\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}` .Calculate the area of ∆ADE and compare it with the area of ∆ABC
In each of the following find the value of 'k', for which the points are collinear.
(7, -2), (5, 1), (3, -k)
In each of the following find the value of 'k', for which the points are collinear.
(8, 1), (k, -4), (2, -5)
Find the missing value:
| Base | Height | Area of triangle |
| 15 cm | ______ | 87 cm2 |
Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.
Find the area of ΔABC with A(1, -4) and midpoints of sides through A being (2, -1) and (0, -1).
Show that the following points are collinear:
A(8,1), B(3, -4) and C(2, -5)
Find the value of y for which the points A(-3, 9), B(2,y) and C(4,-5) are collinear.
If the points (2, -3), (k, -1), and (0, 4) are collinear, then find the value of 4k.
Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is ______.
