Advertisements
Advertisements
प्रश्न
The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.
Advertisements
उत्तर
Hypotenuse = 26 cm
The sum of other two sides is 34 cm.
So, let the other two sides be x cm and (34 – x) cm.
Using Pythagoras theorem,
(26)2 = x2 + (34 – x)2
676 = x2 + x2 + 1156 – 68x
2x2 – 68x + 480 = 0
x2 – 34x + 240 = 0
x2 – 10x – 24x + 240 = 0
x(x – 10) – 24(x – 10) = 0
(x – 10)(x – 24) = 0
x = 10, 24
When x = 10, (34 – x) = 24
When x = 24, (34 – x) = 10
Thus, the lengths the three sides of the right-angled triangle are 10 cm, 24 cm and 26 cm.
संबंधित प्रश्न
The sides of a right-angled triangle containing the right angle are 4x cm and (2x – 1) cm. If the area of the triangle is 30 cm2; calculate the lengths of its sides.
The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:
- the value of x,
- the lengths of its sides,
- its area.
The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.
The perimeter of a rectangle is 104 m and its area is 640 m2. Find its length and breadth.
Two squares have sides x cm and (x + 4) cm. The sum of their area is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.
A farmer has 70 m of fencing, with which he encloses three sides of a rectangular sheep pen; the fourth side being a wall. If the area of the pen is 600 sq. m, find the length of its shorter side.
A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is `7/8` that of the lawn, find the dimensions of the lawn.
In the given figure, the value of x is ______.
If the width of the uniform shaded portion of x m; its area in terms of x is ______.
The length of a rectangle is 3 m more than its width. If its area is 180 m2; the length of the rectangle is ______.
