Advertisements
Advertisements
प्रश्न
In the given figure, ABC is a right angled triangle with ∠BAC = 90°.
- Prove that : ΔADB ∼ ΔCDA.
- If BD = 18 cm and CD = 8 cm, find AD.
- Find the ratio of the area of ΔADB is to area of ΔCDA.
उत्तर
i. Let ∠CAD = x
`=>` m ∠DAB = 90° – x
`=>` m ∠DBA = 180° – (90° + 90° – x) = x
`=>` ∠CDA = ∠DBA ...(1)
In ΔADB and ΔCDA,
∠ADB = ∠CDA ...[Each 90°]
∠ABD = ∠CAD ...[From (1)]
∴ ΔADB ∼ ΔCDA ...[By A.A]
ii. Since the corresponding sides of similar triangles are proportional, we have.
`(BD)/(AD) = (AD)/(CD)`
`=> (18)/(AD) = (AD)/(8)`
`=>` AD2 = 18 × 8 = 144
`=>` AD = 12 cm
iii. The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.
`=> (Ar(ΔADB))/(Ar(ΔCDA)) = (AD^2)/(CD^2)`
= `12^2/8^2`
= `144/64`
= `9/4`
= 9 : 4
APPEARS IN
संबंधित प्रश्न
Given: ABCD is a rhombus, DPR and CBR are straight lines.
Prove that: DP × CR = DC × PR.
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting diagonal AC in L and AD produced in E. Prove that: EL = 2BL.
In the right-angled triangle QPR, PM is an altitude.
Given that QR = 8 cm and MQ = 3.5 cm, calculate the value of PR.
In the given figure, AX : XB = 3 : 5
Find:
- the length of BC, if the length of XY is 18 cm.
- the ratio between the areas of trapezium XBCY and triangle ABC.
An aeroplane is 30 m long and its model is 15 cm long. If the total outer surface area of the model is 150 cm2, find the cost of painting the outer surface of the aeroplane at the rate of Rs.120 per sq. m. Given that 50 sq. m of the surface of the aeroplane is left for windows.
The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their :
- corresponding medians.
- perimeters.
- areas.
On a map, drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has AB = 24 cm and BC = 32 cm. Calculate :
- the diagonal distance of the plot in kilometer.
- the area of the plot in sq. km.
The dimensions of the model of a multistoreyed building are 1 m by 60 cm by 1.20 m. If the scale factor is 1 : 50, find the actual dimensions of the building.
Also, find:
- the floor area of a room of the building, if the floor area of the corresponding room in the model is 50 sq. cm.
- the space (volume) inside a room of the model, if the space inside the corresponding room of the building is 90 m3.
The following figure shows a triangle ABC in which AD and BE are perpendiculars to BC and AC respectively.
Show that:
- ΔADC ∼ ΔBEC
- CA × CE = CB × CD
- ΔABC ~ ΔDEC
- CD × AB = CA × DE
In fig. ABCD is a trapezium in which AB | | DC and AB = 2DC. Determine the ratio between the areas of ΔAOB and ΔCOD.
