Advertisements
Advertisements
प्रश्न
In ΔPQR, ∠Q = 90°, PQ = 12, QR = 5 and QS is a median. Find l(QS).
Advertisements
उत्तर
In △PQR, ∠Q = 90° ...[Given]
△PQR is a right angle triangle.
∴ By Pythagoras theorem,
∴ PR2 = PQ2 + QR2
⇒ PR2 = 122 + 52
⇒ PR2 = 144 + 25
⇒ PR2 = 169
⇒ PR = `sqrt169`
⇒ PR = 13
In △PQR,
seg QS is the median on hypotenuse PR.
∴ QS = `1/2`PR ...[In a right angled triangle, the length of the median on the hypotenuse is half the length of the hypotenuse.]
∴ QS = `1/2 × 13`
∴ QS = 6.5 units
Hence, the length of QS is 6.5 units.
APPEARS IN
संबंधित प्रश्न
The length of hypotenuse of a right angled triangle is 15. Find the length of median of its hypotenuse.
In the given figure, point G is the point of concurrence of the medians of Δ PQR. If GT = 2.5, find the lengths of PG and PT.
In the given figure, point S is any point on side QR of ΔPQR Prove that: PQ + QR + RP > 2PS
Draw an obtuse angled Δ STV. Draw its medians and show the centroid.
Draw an isosceles triangle. Draw all of its medians and altitudes. Write your observation about their points of concurrence.
In any triangle the centroid and the incentre are located inside the triangle
The centroid, orthocentre, and incentre of a triangle are collinear
In the given figure, A is the midpoint of YZ and G is the centroid of the triangle XYZ. If the length of GA is 3 cm, find XA
In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following
If PD = 12, then PN = ?
In ∆DEF, DN, EO, FM are medians and point P is the centroid. Find the following
If DO = 8, then FD = ?
In ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then median of the triangle is ______.
What is a median of a triangle?
What is the point where the medians of a triangle meet called?
The centroid divides each median in what ratio?
In a triangle, where is the centroid always located?
Which statement is true about medians?
