An isosceles right-angled triangle has hypotenuse length as 10 units. What is the area of the triangle (in square units)?
25
Let the legs of the isosceles right-angled triangle be a and a. By Pythagorean theorem, a² + a² = 10² 2a² = 100 a² = 50 a = √50 = 5√2 Area of the triangle = (1/2) * base * height = (1/2) * a * a = (1/2) * a² = (1/2) * 50 = 25
Important Questions from Geometry
The sides of a triangle are in the ratio 6 : 4 : 3 and its perimeter is 104 cm. The length of the longest side (in cm) is:
Two circles of radii 16 cm and 4 cm, respectively, touch each other externally at Point A. PQ is the direct common tangent of these circles with centres C1 and C2, respectively. What is the length of PQ?
Let C be a circle with center O and AB be a chord of C such that the length of AB is equal to the radius of C. Let D be any point on the major arc of AB. Find ∠AOB and ∠ADB, respectively.
The centres of two circles are 84 cm apart. If the radii of these two circles are 38 cm and 26 cm, respectively, then which of the following options gives the length (in cm) of a direct common tangent of these two circles?
In ADEF, the bisector of ∠D intersects side EF at point N. If DE = 36 cm, DF = 40 cm and EF = 38 cm, then the length (in cm) of NF is ________.
