Advertisements
Advertisements
प्रश्न
In each of the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in each figure. Determine x, y, z in each case.
उत्तर
Δ PQR is a right triangle, right angled at Q
`6+z^2 = (4+x)^2`
`6+z^2=16+x^2+8x`
`z^2-x^2-8x=16-36`
`z^2-x^2-8x=16-36`
`z^2-x^2-8x=-20`......(1)
Δ QSP is a right triangle right angled at S
`QS^2+PS^2=PQ^2`
`y^2+4^2=6^2`
`y^2+16=36`
`y^2=36-16`
`y^2=20`
`y=sqrt20`
`y=sqrt(2xx2xx5)`
`y=2sqrt5`
Δ QSR is a right triangle right angled at S
`QS^2+RS^2=QR^2`
`y^2+x^2=z^2`..........(2)
Now substituting `y^2+x^2=z^2` in equation (i) we get
`y^2+x^2-x^2-8x=-20`
`20-8x=-20`
`-8x=-20-20`
`-8x=-40`
`x=40/8`
`x=5`
Now substituting ` x = 5` and `y^2=20` in equation (ii) we get
`y^2+x^2=z^2`
`20+5^2=z^2`
`20+25=z^2`
`45=z^2`
`sqrt(3xx3xx5)=z^2`
`3sqrt5=z`
Hence the value of x, y and z are `5,2sqrt5,3sqrt5`
APPEARS IN
संबंधित प्रश्न
the below given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of ΔABC is 54 cm2, then find the lengths of sides AB and AC.
In the below figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of Δ ABC is 54 cm2, then find the lengths of sides AB and AC.
In below Figure, ΔABC is right angled at C and DE ⊥ AB. Prove that ΔABC ~ ΔADE and Hence find the lengths of AE and DE.
In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :
In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :
Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, determine the area of the larger triangle.
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the road. Assuming that her string (from the tip of her road to the fly) is taut, how much string does she have out (in the given figure)? If she pulls the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 seconds.
If ∆ABC and ∆DEF are two triangles such tha\[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{2}{5}\] , then Area (∆ABC) : Area (∆DEF) =
∆ABC is a right triangle right-angled at A and AD ⊥ BC. Then, \[\frac{BD}{DC} =\]
∆ABC is such that AB = 3cm, BC = 2cm, CA = 2.5cm. If ∆ABC ~ ∆DEF and EF = 4cm, then perimeter of ∆DEF is ______.
