Advertisements
Advertisements
Question
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height
Advertisements
Solution
In an isosceles triangle the altitude dives its base into two equal parts.
Now in the figure, ∆ABC is an isosceles triangle with AD as its height
In the figure, AD is the altitude and ∆ABD is a right triangle.
By Pythagoras theorem,
AB2 = AD2 + BD2
⇒ AD2 = AB2 – BD2
= 132 – 122 = 169 – 144 = 25
AD2 = 25 = 52
Height: AD = 5 cm
APPEARS IN
RELATED QUESTIONS
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 7 cm, 24 cm, 25 cm
In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices ?
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
In Fig. 3, ∠ACB = 90° and CD ⊥ AB, prove that CD2 = BD x AD.
Find the Pythagorean triplet from among the following set of numbers.
4, 5, 6
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.
For going to a city B from city A, there is a route via city C such that AC ⊥ CB, AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
In ∆PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a – b) = (c + d)(c – d).
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
