Advertisements
Advertisements
Question
In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.
Advertisements
Solution
In ΔSRQ, ∠R = 90°
∴ QS2 = RS2 + QR2 ....(Pythagoras Theorem)
= 202 + 212
= 440 + 441
= 841
Now,
In ΔQSP, ∠P = 90°
∴ QS2 = PQ2 + PS2
⇒ QS2 = PQ2 + PQ2 ....(Pythagoras Theorem)
⇒ QS2 = 2PQ2 ....(Given PQ = PS)
⇒ PQ2 = `"QS"^2/(2) = (841)/(2)` = 420.5
⇒ PQ = 20.50cm.
APPEARS IN
RELATED QUESTIONS
ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2= AC2 + BD2
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 Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD2 = BD × CD
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]
km. Find their speed per hour.
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL2 + CM2) = 5 BC2
Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.
If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ2 + BP2 ) = (AB2 + PQ2)
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
The sides of the triangle are given below. Find out which one is the right-angled triangle?
40, 20, 30
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
Find the length of the support cable required to support the tower with the floor
Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.
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.
